Day-Ahead Probabilistic Forecast of Solar Irradiance: A Stochastic Differential Equation Approach

  • Jordi Badosa
  • Emmanuel GobetEmail author
  • Maxime Grangereau
  • Daeyoung Kim
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 254)


In this work, we derive a probabilistic forecast of the solar irradiance during a day at a given location, using a stochastic differential equation (SDE for short) model. We propose a procedure that transforms a deterministic forecast into a probabilistic forecast: the input parameters of the SDE model are the AROME numerical weather predictions computed at day \(D-1\) for the day D. The model also accounts for the maximal irradiance from the clear sky model. The SDE model is mean-reverting towards the deterministic forecast and the instantaneous amplitude of the noise depends on the clear sky index, so that the fluctuations vanish as the index is close to 0 (cloudy) or 1 (sunny), as observed in practice. Our tests show a good adequacy of the confidence intervals of the model with the measurement.


Solar power Probabilistic forecast Stochastic differential equation 



This research is part of the Chair Financial Risks of the Risk Foundation, the Finance for Energy Market Research Centre and the ANR project CAESARS (ANR-15-CE05-0024). The work benefits from the support of the Siebel Energy Institute and it was conducted in the frame of the TREND-X research program of Ecole Polytechnique, supported by Fondation de l’Ecole Polytechnique. The authors acknowledge Météo-France and the Cosy project for the numerical weather prediction data used in the study.


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jordi Badosa
    • 1
  • Emmanuel Gobet
    • 2
    Email author
  • Maxime Grangereau
    • 2
  • Daeyoung Kim
    • 3
  1. 1.LMD/IPSL, Ecole PolytechniquePalaiseau CedexFrance
  2. 2.CMAP, Ecole PolytechniquePalaiseau CedexFrance
  3. 3.Ecole PolytechniquePalaiseau CedexFrance

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